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FAD 1013. INDICES, SURDS AND LOGARITHMS WEEK 1 (L2 & L3) Sir JEDZRY.
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“exponent” or “index” (plural “indices”). “Base”.
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5 appears 2 times.. It is possible for the exponent to be fractional, 0 or negative..
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4. INDICES: Rules/Properties. abstract. abstract.
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Simplify the following.. 1. Questions on provided worksheet..
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Introduction to exponent. A black text with a white background Description automatically generated.
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Rational roots. -3 is the 5th root of -243 since (-3)5 =-243..
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8. EXAMPLE 1.
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EXAMPLE 2.
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[Audio] Remind students of the general form of each result where a is any number and m and n are integers..
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11. SURDS. radical symbo radicand 2 index—O radical.
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12. Properties of nth Roots Property = a if n is odd a I if n is even Example 16 2 3 (-5)3 = -5.
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When simplifying expression related to surds, make sure to rationalise the denominator => get rid of the radical sign in the denominator..
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EXAMPLE 3. Rationalize the following expressions..
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EXAMPLE 4. Simplify the following:.
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Log of x to the base a is y. abstract. Note: log of negatives and zero are not Defined in Reals.
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Laws of Logarithms. PROPERTIES OF LOGARITHMS. abstract.
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EXAMPLE 5.
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EXAMPLE 6.
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CHANGE OF BASE FORMULA-DERIVATION.
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EXAMPLE 7.
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SOLVING INDEX EQUATIONS.
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EXAMPLE 8.
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EXAMPLE 9.
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EXAMPLE 10.
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SOLVING RADICAL EQUATIONS. How to solve: Leave one of the terms with surd on one side and all other terms on the other. Square both sides of the equation and simplify. Repeat step 1 and step 2 if there is more than one term with surd (until all the surds are removed). Check the solution (true solutions of the original equation). Values which do not satisfy the equation = extraneous solutions (not a valid solution)..
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EXTRANEOUS SOLUTION.
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EXAMPLE 11.
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SOLVING LOGARITHMIC EQUATIONS. The properties of log are used to simplify and solve the equations..
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EXAMPLE 12.
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EXAMPLE 13.
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Reminder !!!!. Quadratic Equation is an equation with maximum degree of variable 2..
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33. _ ællAlyavad&21u P,iyanæ? ')tJZö.